Shane Johnson

Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams

In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load.

An Ergonomic Testing System for the First Metatarsophalangeal Joint Stiffness

Osteoarthritis sufferers commonly have first metatarsophalangeal joint (MTPJ) problems in which articular surfaces are changed permanently due to fatigue. Therefore, medical devices for early diagnosis would increase the opportunity for prevention of disease progression. In previous studies on stiffness of the first MTPJ many details, although functionally of great importance, have not been fully considered including: design and size of the device, tribology consideration, and errors from device. Therefore, the motivation of our research was to enhance the device design by reducing the size of the device, and device design was enhanced by minimizing measurement errors through development of a new ergonomic left and right foot instrument located medial to the first MTPJ (instead of beneath the foot). The first MTPJ stiffness (N mm/kg radian) measurement was taken on 28 subjects with two replicates per subject by the same tester. The first MTPJ stiffness ranged from 3.49 to 14.42 N mm/kg radian with the mean (SD) value of 8.28 (3.15) N mm/kg radian for the left feet and 3.91 to 11.90 N mm/kg radian with the mean (SD) value of 7.65 (2.07) N mm/kg radian for the right feet. Reliability evaluation was measured using intraclass correlation coefficient and described an excellent reliability between two tests.

Region-specific constitutive modeling of the plantar soft tissue

Recent research has shown that hyperelastic properties of the plantar soft tissue consisting of adipose tissue and fibrous septa change from region to region. However, relatively little research has been conducted to develop analytical or computational models to describe the region-specific behavior of the plantar soft tissue. The objective of the research is to develop a region-specific constitutive model of the plantar soft tissue. Plantar soft tissue specimens were dissected from six regions [subcalcaneal (CA), sublateral (LA), subnavicular (Nav), 1st, 3rd, and 5th submetatarsal (M1, M3, M5)] from cadaveric foot samples, and a picrosirius red staining technique was used to visualize the collagen fibers in fibrous septa. The volume fractions of adipose tissue and fibrous septa and the volume fractions of the principal orientations of the fibrous septa were calculated with the intensity gradient method. Region-specific constitutive models were then developed in finite element analysis considering the microstructure of the plantar soft tissue. The hyperelastic region specific material properties of the plantar soft tissue were validated with experimental unconfined compression tests and indentation tests from the literature. The results show that the models give reasonable predictions of the stiffness of the soft tissue within a standard deviation of the tests. The region-specific constitutive models help to explain how changes in the constituents are related to mechanical behavior of the soft tissue on a region specific basis.

Experimental and computational analysis of orthotic medial longitudinal arch support height

Lower extremity injuries (LEI) in the foot and ankle region are the most common injuries experienced by physically active groups (including sports and military personnel). Classical treatment for L...

Effects of boundary conditions on foot behaviour in the standing position in 3D finite element foot model

The most common physical injuries are injuries of the lower extremity. In fact, controlled studies on highly physically active groups such as athletes and military personnel show that five injury types are repeatedly cited as accounting for over 50 percent of all training injuries: stress fractures, overuse injuries of the knee, Plantar Fasciitis, Achilles Tendonitis, and ankle sprains [1-5]. Three-dimensional finite element analysis (3D FEA) of the foot in the standing position allows researchers to analyze the relationship between foot behavior and orthotic designs, which may help to relieve or prevent such injuries. Various 3D FEA models of the foot in the standing position show very different boundary conditions, including: fixing the fibula and tibia at different points between the ankle and knee, fixing the talus, and applying slip/no-slip conditions in the articular surfaces [6-12]. This may have a large effect on overall foot stiffness and the strain of the Plantar Aponeurosis. This study is developed to investigate the influence of these boundary conditions on the overall foot stiffness and strain in the Plantar Aponeurosis in the standing position.